The Effect of the Boundary Conditions in the Reformulation of QCD_4

TL;DR

This paper explores how boundary conditions influence the phase structure of QCD_4 when reformulated as a topological quantum field theory, revealing the role of U(1) backgrounds in phase behavior under special gauge choices.

Contribution

It demonstrates the impact of boundary conditions on the phase structure of QCD_4 reformulated via TQFT and highlights the significance of U(1) backgrounds in this context.

Findings

Deconfining phase possible with twisted boundary conditions

Perturbative parts screen the deconfining phase

U(1) background encodes phase structure information

Abstract

We discuss the phase structure of QCD_4 as a perturbative deformation of the Topological Quantum Field Theory (TQFT). When we choose a special Maximal Abelian gauge (MAG) as the gauge fixing, the TQFT sector is equivalent to a 2D O(3) non-linear sigma model (NLSM). We consider the finite temperature case, and investigate the effect of the boundary conditions and the phase structure of the TQFT sector. It can have a deconfining phase under the twisted boundary conditions. However, this phase is screened once pertubative parts are added. We conclude that the information about the phase structure is encoded in the U(1) background in the case of the MAG.